mie376mid11

# mie376mid11 - MIE376 Mathematical Programming Mid-Term Exam...

This preview shows pages 1–2. Sign up to view the full content.

MIE376 – Mathematical Programming Mid-Term Exam February 15, 2011 Note: Clearly state any assumptions you make in answering any of the questions below. 1) Consider the following LP problem: Max 5x 1 + 3x 2 + x 3 subject to 3x 1 + 2x 2 + x 3 7 ; x 2 + x 3 ≤ 3; x 1 + x 3 ≤ 2 ; and x 1 , x 2, x 3 ≥ 0 a) Determine the optimal solution using 3 iterations of the Revised Simplex method b) Evaluate and interpret the Shadow Prices and Reduced Costs c) Formulate the Dual of this LP d) Derive the optimal solution of the Dual from the Optimal Solution of the Primal. Z = c B T B -1 b – (c B T B -1 N – c N ) 2) Consider the following Bi-level LP problem: Min 3x 1 + x 2 such that 1 ≤ x 2 ≤ 6; and x 1 is the optimal solution of the following LP Max x 1 subject to x 1 + x 2 ≤ 8; 4x 1 + x 2 ≥ 8; 2x 1 + x 2 ≤ 13; and x 1 ≥ 0 a) Use KKT conditions to derive an equivalent mathematical programming problem. b)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/20/2011 for the course MIE 376 taught by Professor Daniel during the Spring '11 term at University of Toronto.

### Page1 / 2

mie376mid11 - MIE376 Mathematical Programming Mid-Term Exam...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online